Total Surface Area of Great Stellated Dodecahedron given Pentagram Chord Calculator

✖Pentagram Chord of Great Stellated Dodecahedron is the distance between any pair of non adjacent peak vertices of the pentagram corresponding to the Great Stellated Dodecahedron.ⓘ Pentagram Chord of Great Stellated Dodecahedron [l_c(Pentagram)]

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✖Total Surface Area of Great Stellated Dodecahedron is the total quantity of plane enclosed by the entire surface of the Great Stellated Dodecahedron.ⓘ Total Surface Area of Great Stellated Dodecahedron given Pentagram Chord [TSA]

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Total Surface Area of Great Stellated Dodecahedron given Pentagram Chord Solution

STEP 0: Pre-Calculation Summary

Formula Used

Total Surface Area of Great Stellated Dodecahedron = 15*sqrt(5+(2*sqrt(5)))*(Pentagram Chord of Great Stellated Dodecahedron/(2+sqrt(5)))^2
TSA = 15*sqrt(5+(2*sqrt(5)))*(l_c(Pentagram)/(2+sqrt(5)))^2
This formula uses 1 Functions, 2 Variables

Functions Used

sqrt - A square root function is a function that takes a non-negative number as an input and returns the square root of the given input number., sqrt(Number)

Variables Used

Total Surface Area of Great Stellated Dodecahedron - (Measured in Square Meter) - Total Surface Area of Great Stellated Dodecahedron is the total quantity of plane enclosed by the entire surface of the Great Stellated Dodecahedron.
Pentagram Chord of Great Stellated Dodecahedron - (Measured in Meter) - Pentagram Chord of Great Stellated Dodecahedron is the distance between any pair of non adjacent peak vertices of the pentagram corresponding to the Great Stellated Dodecahedron.

STEP 1: Convert Input(s) to Base Unit

Pentagram Chord of Great Stellated Dodecahedron: 42 Meter --> 42 Meter No Conversion Required

STEP 2: Evaluate Formula

Substituting Input Values in Formula

TSA = 15*sqrt(5+(2*sqrt(5)))*(l_c(Pentagram)/(2+sqrt(5)))^2 --> 15*sqrt(5+(2*sqrt(5)))*(42/(2+sqrt(5)))^2

Evaluating ... ...

TSA = 4538.24522956981

STEP 3: Convert Result to Output's Unit

4538.24522956981 Square Meter --> No Conversion Required

FINAL ANSWER

4538.24522956981 ≈ 4538.245 Square Meter <-- Total Surface Area of Great Stellated Dodecahedron

(Calculation completed in 00.004 seconds)

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Walchand College of Engineering (WCE), Sangli

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Indian Institute of Information Technology (IIIT), Bhopal

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< Surface Area of Great Stellated Dodecahedron Calculators

Total Surface Area of Great Stellated Dodecahedron given Circumradius

LaTeX Go Total Surface Area of Great Stellated Dodecahedron = 15*sqrt(5+(2*sqrt(5)))*((4*Circumradius of Great Stellated Dodecahedron)/(sqrt(3)*(3+sqrt(5))))^2

Total Surface Area of Great Stellated Dodecahedron given Ridge Length

LaTeX Go Total Surface Area of Great Stellated Dodecahedron = 15*sqrt(5+(2*sqrt(5)))*((2*Ridge Length of Great Stellated Dodecahedron)/(1+sqrt(5)))^2

Total Surface Area of Great Stellated Dodecahedron given Pentagram Chord

LaTeX Go Total Surface Area of Great Stellated Dodecahedron = 15*sqrt(5+(2*sqrt(5)))*(Pentagram Chord of Great Stellated Dodecahedron/(2+sqrt(5)))^2

Total Surface Area of Great Stellated Dodecahedron

LaTeX Go Total Surface Area of Great Stellated Dodecahedron = 15*sqrt(5+(2*sqrt(5)))*Edge Length of Great Stellated Dodecahedron^2

Total Surface Area of Great Stellated Dodecahedron given Pentagram Chord Formula

LaTeX Go

Total Surface Area of Great Stellated Dodecahedron = 15*sqrt(5+(2*sqrt(5)))*(Pentagram Chord of Great Stellated Dodecahedron/(2+sqrt(5)))^2
TSA = 15*sqrt(5+(2*sqrt(5)))*(l_c(Pentagram)/(2+sqrt(5)))^2

What is Great Stellated Dodecahedron?

The Great Stellated Dodecahedron is a Kepler-Poinsot polyhedron, with Schläfli symbol {⁵⁄₂,3}. It is one of four nonconvex regular polyhedra. It is composed of 12 intersecting pentagrammic faces, with three pentagrams meeting at each vertex.

How to Calculate Total Surface Area of Great Stellated Dodecahedron given Pentagram Chord?

Total Surface Area of Great Stellated Dodecahedron given Pentagram Chord calculator uses Total Surface Area of Great Stellated Dodecahedron = 15*sqrt(5+(2*sqrt(5)))*(Pentagram Chord of Great Stellated Dodecahedron/(2+sqrt(5)))^2 to calculate the Total Surface Area of Great Stellated Dodecahedron, Total Surface Area of Great Stellated Dodecahedron given Pentagram Chord formula is the total quantity of plane enclosed by the entire surface of the Great Stellated Dodecahedron, calculated using its pentagram chord. Total Surface Area of Great Stellated Dodecahedron is denoted by TSA symbol.

How to calculate Total Surface Area of Great Stellated Dodecahedron given Pentagram Chord using this online calculator? To use this online calculator for Total Surface Area of Great Stellated Dodecahedron given Pentagram Chord, enter Pentagram Chord of Great Stellated Dodecahedron (l_c(Pentagram)) and hit the calculate button. Here is how the Total Surface Area of Great Stellated Dodecahedron given Pentagram Chord calculation can be explained with given input values -> 4538.245 = 15*sqrt(5+(2*sqrt(5)))*(42/(2+sqrt(5)))^2.

FAQ

What is Total Surface Area of Great Stellated Dodecahedron given Pentagram Chord?

Total Surface Area of Great Stellated Dodecahedron given Pentagram Chord formula is the total quantity of plane enclosed by the entire surface of the Great Stellated Dodecahedron, calculated using its pentagram chord and is represented as TSA = 15*sqrt(5+(2*sqrt(5)))*(l_c(Pentagram)/(2+sqrt(5)))^2 or Total Surface Area of Great Stellated Dodecahedron = 15*sqrt(5+(2*sqrt(5)))*(Pentagram Chord of Great Stellated Dodecahedron/(2+sqrt(5)))^2. Pentagram Chord of Great Stellated Dodecahedron is the distance between any pair of non adjacent peak vertices of the pentagram corresponding to the Great Stellated Dodecahedron.

How to calculate Total Surface Area of Great Stellated Dodecahedron given Pentagram Chord?

Total Surface Area of Great Stellated Dodecahedron given Pentagram Chord formula is the total quantity of plane enclosed by the entire surface of the Great Stellated Dodecahedron, calculated using its pentagram chord is calculated using Total Surface Area of Great Stellated Dodecahedron = 15*sqrt(5+(2*sqrt(5)))*(Pentagram Chord of Great Stellated Dodecahedron/(2+sqrt(5)))^2. To calculate Total Surface Area of Great Stellated Dodecahedron given Pentagram Chord, you need Pentagram Chord of Great Stellated Dodecahedron (l_c(Pentagram)). With our tool, you need to enter the respective value for Pentagram Chord of Great Stellated Dodecahedron and hit the calculate button. You can also select the units (if any) for Input(s) and the Output as well.

How many ways are there to calculate Total Surface Area of Great Stellated Dodecahedron?

In this formula, Total Surface Area of Great Stellated Dodecahedron uses Pentagram Chord of Great Stellated Dodecahedron. We can use 3 other way(s) to calculate the same, which is/are as follows -

Total Surface Area of Great Stellated Dodecahedron = 15*sqrt(5+(2*sqrt(5)))*Edge Length of Great Stellated Dodecahedron^2
Total Surface Area of Great Stellated Dodecahedron = 15*sqrt(5+(2*sqrt(5)))*((2*Ridge Length of Great Stellated Dodecahedron)/(1+sqrt(5)))^2
Total Surface Area of Great Stellated Dodecahedron = 15*sqrt(5+(2*sqrt(5)))*((4*Circumradius of Great Stellated Dodecahedron)/(sqrt(3)*(3+sqrt(5))))^2

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